Nonstandard Analysis

Nonstandard analysis is a reformulation of calculus that uses a logically rigorous notion of infinitesimal numbers, rather than defining the operations of calculus purely through limits as the standard approach does. It originated in the early 1960s with the mathematician Abraham Robinson, who argued that the law of continuity formulated by Gottfried Wilhelm Leibniz anticipated what Robinson called the transfer principle, and that the informal infinitesimals used during calculus's formative years could be given a rigorous foundation through the tools of contemporary model theory. The approach vindicates Leibniz's original intuition about infinitely small quantities and has been applied productively to classical analysis and to other branches of mathematics. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/